You are given an account in which the force of interest is described by the formula δt =(1+t) ^(−1/2) for t ≥ 0. The amount in the account at time 0 is β(0)=1, and in general the amount at time t, for t ≥ 0, is denoted by β(t). For t > 0, deposits are made into the account continuuosly, at the rate α(t)= β(t)⋅(1+t)^(−3/2). Find β(8).